Optimal representation of piecewise Hölder smooth bivariate functions by the Easy Path Wavelet Transform

• Autores: Gerlind Plonka, Armin Iske, Stefanie Tenorth
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 176, Nº 1, 2013, págs. 42-67
• Idioma: inglés
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• Resumen

  • The Easy Path Wavelet Transform (EPWT) (Plonka, 2009) [26] has recently been proposed by one of the authors as a tool for sparse representations of bivariate functions from discrete data, in particular from image data. The EPWT is a locally adaptive wavelet transform. It works along pathways through the array of function values and it exploits the local correlations of the given data in a simple appropriate manner. In this paper, we aim to provide a theoretical understanding of the performance of the EPWT. In particular, we derive conditions for the path vectors of the EPWT that need to be met in order to achieve optimal N-term approximations for piecewise H¨older smooth functions with singularities along curves.